I went through a very similar dilemma about a year back concerning the 70-200 f/2.8, whether or not I needed the bulky zoom and it's f/2.8. Nick5 weighed in on my thread too
In the end, I kept the f/2.8 because it's a fantastic lens, but I also resigned myself to the fact that it's just too bulky and reach-limited for travel usage. It is a studio/portrait/photojournal lens that doesn't leave the house all that often, but when it does, it delivers.
The first thing you need to address is what you are going to do with the 70-200 f/2.8: do you absolutely need to sell it to fund your next purchase, or are you looking to hold onto it and add another lens?
Next, you already have a Sigma 150-600 coming that will take care of your wildlife needs, but I take it you won't be traveling with it for the same reasons you don't travel with the 70-200?
That will make your lineup look like this:
18-135
70-200 f/2.8
150-600
So, that leaves you wanting a lens dedicated to 1) travel 2) wildlife. Here's the thing about going with another 70-200: when you aren't traveling, will it get enough use? Also, I feel that the 200mm long end falls well short of what you'd need for wildlife, but since you didn't tell us exactly what kind of wildlife, I could be wrong (birds vs. elephants, for example).
Depending on your budget (i.e. do you sell the 70-200) I'd go with either the above-suggested 55-250 STM, or the 70-300L, over the 70-200 f/4. Good comparison: http://dancarrphotography.com …review-vs-70-200-f4-l-is/
If someday I stumble upon a lot of money and vacation time, and start traveling a lot (none of which are likely), I'd globe trot with a 16-35 f/4, 50mm prime, and the 70-300L.